Question

0.10mM${\mathbf{KMnO}}_{\mathbf{4}}$has an absorbance maximum of 0.26 at 525 nm in a

1.000-cm cell. Find the molarabsorptiveand the concentration of a solution whose

absorbance is 0.52 at 525 nm in the same cell.

Short answer

The value of molar absorptive is$2600{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$

The value of solution absorbance is$0.2\mathrm{mM}$

Step-by-step solution

Calculate molar absorptive:

Equation to calculate ε is,

$\mathrm{\epsilon }=\frac{\mathrm{A}}{\mathrm{bc}}$ →(1)

Given,

$$\begin{gathered} \mathrm{c}=0.10\mathrm{mM} \\ \mathrm{b}=1.000\mathrm{cm} \\ \mathrm{A}=0.26 \end{gathered}$$

Substitute in equation (1),

$$\begin{gathered} \mathrm{\epsilon }=\frac{0.26}{\left(1.000\mathrm{cm}\right)\left(0.10\mathrm{mM}\right)\left[{\displaystyle \frac{{10}^{-3}\mathrm{M}}{1\mathrm{mM}}}\right]} \\ \mathrm{\epsilon }=2600{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1} \end{gathered}$$

The value of molar absorptive is $2600{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$

Calculate solution concentration:

Equation for concentration is $\mathrm{c}=\frac{\mathrm{A}}{\mathrm{bc}}$

Given,

$$\begin{gathered} \mathrm{b}=1.000\mathrm{cm} \\ \mathrm{A}=0.26 \\ \mathrm{\epsilon }=2600{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1} \end{gathered}$$

Substitute in above equation,

$$\begin{gathered} \mathrm{c}=\frac{0.52}{\left(1.000\mathrm{cm}\right)\left(2600{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}\right)} \\ =\left(0.0002\mathrm{M}\right)\left[\frac{{10}^3\mathrm{mM}}{1\mathrm{M}}\right] \\ \mathrm{c}=0.2\mathrm{mM} \end{gathered}$$

The value of solution absorbance is$0.2\mathrm{mM}$